Modeling of an industrial wet grinding operation using data-driven techniques
Introduction
Grinding plays a critical role in most of the ore beneficiation operations in mineral processing plants. As the size of the particles produced by grinding operation becomes the driver for the performance indicators for the operation of the following units, flotation in this case, modeling and thereafter the control of the grinding operation of industrial scale has been a continuous endeavor of the mineral engineers. Over the years, the modeling of grinding operation has attained a reasonable state of robustness (Herbst & Fuerstenau, 1973; Herbst, Siddique, Rajamani, & Sanchez, 1983; Kinneberg & Herbst, 1984; Lynch & Rao, 1975; Rajamani and Herbst, 1984, Rajamani and Herbst, 1991a). Most of the cases, these approaches follow the hybrid path of physical and empirical routes where mass balance of the materials is carried out using physical laws and the separation kinetics are modeled using empirical methods. Using these kind of modeling approaches and the resulting models, research has been carried out on several aspects of single as well as multiple objective optimization and control of industrial grinding operations (Birch, 1972; Bryson & Ho, 1969; Herbst & Rajamani, 1979; Lapidus & Luss, 1967; Rajamani & Herbst, 1991b; Mitra & Gopinath, 2004). These kind of hybrid grinding models are reported to work really well in many cases (Mitra & Gopinath, 2004) if tuned properly with the plant using the data obtained from hardware sensors in at least some bare minimum flow streams. Moreover, hybrid modeling approaches have a lot of parameters in empirical correlations that need tuning using plant data in almost every important stream leading to a huge requirement of data. Unfortunately, many of the industrial grinding operations lack in adequate hardware sensors for many important intermediate streams and have a few sensors only in the input and final product streams. This makes the tuning process of empirical parameters used in case of modeling various unit operations within grinding circuit (e.g. grinding, hydrocyclones, etc.) extremely difficult leading to a challenging task of physically modeling the grinding operation. Above this, a multi-variable system identification of the plant operation is very badly needed to control a grinding operation successfully, as control of industrial grinding operation is fairly non-linear in nature and difficult to control. To meet the need of the scenarios stated above where lack of hardware sensor becomes bottleneck to build a phenomenological model of the grinding process, some form of system identification based on data-driven modeling procedures come to rescue to deploy control system to operate the plant efficiently. The data-based modeling strategies proposed here are based on artificial neural networks (ANN) and wavelets-based networks. These techniques offer interesting possibilities for performing the system identification as they provide structures for function approximation with learning capability.
Methods based on neural networks have been proposed as useful tools for process modeling, diagnosis, data rectification and control (Karjala & Himmelblau, 1994; Himmelblau & MacMurray, 1993; Pollard, Broussard, Garrison, & San, 1992; Bhat & McAvoy, 1990). These methods have strong potential to perform rapid and non-linear system identification based on historical data and form the nonparametric models. Neural networks, modeled after neurons in brain, provide general computational models, the densely interconnected simple processing units called as neurons, which carry out the computations in a distributed manner. Many different models of neural network exist, each one having its own feature and applications. Neural networks provide significant benefits like non-linear modeling, learning, robustness, and compactness (Narendra & Parthasarathy, 1990). Most neural network applications fall into four categories: pattern recognition (classification, restoration), associative memory, optimization, and function approximation. The ANN techniques used here are mainly for handling function approximation type of scenarios.
Neural networks provide an effective way of initializing the identification. A trained neural network could predict the parameter values called as weights associated with process input and output data and this type of network forms a feed-forward identifier. A generic ANN consists of several layers of interconnected neurons. In feed-forward neural network (FNN), three types of layers can be distinguished: the input layer (the first layer), the output layer (the final layer) and hidden layers (layers of neuron between the input and output layer). The output of the neuron is determined by functions called as activation functions, which may be non-linear such as sigmoid activation function or squashing (logistic) function. Each neuron produces a weighted sum of its inputs giving a net result and this net result upon operation by activation function produces the output without any feedback. ANN application development mainly has three phases: the training phase, the testing phase and the users (validation) phase. The training phase determines the weights based on input training pattern, the testing phase calculates output pattern compared against target pattern and the validation phase contains application to an unknown problem. FNN acts as pattern associators and generate a functional relationship that correlates a set of input vectors with its corresponding output vectors. The second type of neural networks considered here is recurrent neural network (RNN). RNNs are capable of representing non-linear dynamical systems (Pan, Sung, & Lee, 2001). These networks employ a feedback path providing dynamic behavior and the feedback mechanism exists during training as well as normal operation phase. RNNs produce an output and feed it back to modify the input and a new output is generated. Thus, both the techniques described above offer the possible opportunity of data-based modeling of grinding circuit, which inherently represent non-linear behavior.
Another class of identification technique applied here is topology-using wavelets as activation functions (Daubechies, 1992). This technique is considered as a powerful tool for use in analysis and synthesis of functions. A discussion on process control-related identification technique based on wavelets is reported in (Carrier & Stephanopoulos, 1998). A wavelet is a member of an infinite set of functions with finite support and thus has an ability to perform local analysis. It allows the use of long time intervals for precise low frequency information and short time intervals for high frequency information. Wavelets form wavelet family that can be used as tool in function analysis and synthesis. The concept is similar to a set of sine functions at different frequencies as used in Fourier analysis. In order to consider large input dimensions of a given problem, practical implementation of multidimensional wavelets is required. This job is performed by wavelet frames and complete analysis of the same can be found in (Zhang, 1997). One such frame is called as wavenet. A wavenet is a network with activation functions derived from class of wavelets. It overcomes some of the disadvantages of conventional ANN. Parallel development of the same is reported by (Bakshi & Stephanopoulos, 1993; Zhang & Benveniste, 1992). Some wavelet families are associated with scaling functions, which perform coarse approximation at the lowest frequency, and additional wavelets are introduced then to capture the details. The multiresolution nature of the wavelet basis functions combines the benefits of global as well as local approximation, which enables them to model the high as well as low frequency components present in the behavior of the given system. Hence application of this technique is explored here to see its applicability for data-driven modeling of non-linear behavior of grinding circuits.
The industrial grinding operation under consideration is a part of lead–zinc ore beneficiation process. Ore beneficiation is carried out in mainly two stages: grinding and flotation. Pulverization of the ore to finely ground particles in wet grinding mills is performed in order to liberate the valuables, i.e. lead and zinc, from its associated gangue. The ground particles are then selectively floated in flotation cells for individual recovery of lead and zinc by various means of physical and chemical separation. The grinding circuit has:
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a rod mill in open circuit operation,
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a ball mill in closed circuit operation, and
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a two-stage classification unit (one hydrocyclone for the primary classification and two hydrocyclones in parallel for the secondary classification).
After crushing in primary and secondary crushers, the ore from the mine is sent to fine ore storage bin. Fresh ore feed from the fine ore storage bin along with water is fed to the rod mill. The rod mill discharge slurry is mixed with the ball mill discharge slurry in a sump known as the primary sump. Water is added to the primary sump to reduce the pulp density to facilitate the flow of the slurry smoothly within the circuit. The slurry from the primary sump is fed to primary cyclone, the primary classification unit. The overflow from the primary cyclone goes to another sump, namely secondary sump, where water is added to lower pulp density further. The mixed slurry from the secondary sump is fed to the secondary cyclone, the secondary classification unit. The underflow product from both primary and secondary cyclones is fed to the ball mill. The overflow from the secondary cyclone is the final product from the grinding circuit and goes to flotation circuit as feed. The complete circuit configuration is given in Fig. 1. In this circuit, only the input and output streams are having the hardware sensors (as shown by black circles in Fig. 1) that can indicate the status of key performance indicators (KPI) of the circuit (some properties of slurry at the final product stream) dynamically.
Section snippets
Formulation
In the grinding circuit presented in Fig. 1, three main inputs that are manipulated to control the grinding operation (manipulated variables) are solid stream of raw ore and water streams going to primary and secondary sumps. The circuit has only one output that is secondary cyclone overflow stream. The five KPIs identified for grinding circuit control are throughput (output 1), percentages of three size classes (+150 μm, −63 μm, and −38 μm), i.e. outputs 2, 3, and 4, respectively, and percent
Results and discussions
The data for KPI values for grinding circuit final output stream are generated using hybrid grinding model (Mitra & Gopinath, 2004) by applying different input patterns to it. More than 20 cases were tested and results of some of them are presented in following tables. The input patterns of the MVs were randomly generated so as to cover the all-possible frequencies that may be involved in actual plant operation (Kane, 1999). Excitation is given to three MVs within their respective operating
Conclusions
Data-driven techniques are applied for modeling of an industrial Pb–Zn grinding operation. All the six KPIs were modeled using three inputs. Both techniques are found to be good at fitting the data. This gives a confidence in applying data-based modeling techniques to industrial grinding operations. Additionally it saves time on building first principles models, find the required physical parameters and validate the models. Whenever a control strategy is implemented for a particular process,
Acknowledgement
Authors acknowledge Mr. Shivram Kamat and Mrs. Jessy Smith for their continuous knowledge sharing on ANN and wavelet analysis and support by Dr. Gautam Sardar in course of this work.
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